Purpose The purpose of this paper is to comprehensively evaluate the progress in the development of trapped vortex combustors (TVCs) in the past three decades. The review aims to identify the needs, predict the scope and discuss the challenges of numerical simulations in TVCs applied to gas turbines. Design/methodology/approach TVC is an emerging combustion technology for achieving low emissions in gas turbine combustors. The overall operation of such TVCs can be on very lean mixture ratio and hence it helps in achieving high combustion efficiency and low overall emission levels. This review introduces the TVC concept and the evolution of this technology in the past three decades. Various geometries that were explored in TVC research are listed and their operating principles are explained. The review then categorically arranges the progress in computational studies applied to TVCs. Findings Analyzing extensive literature on TVCs the review discusses results of numerical simulations of various TVC geometries. Numerical simulations that were used to optimize TVC geometry and to enhance mixing are discussed. Reactive flow studies to comprehend flame stability and emission characteristics are then listed for different TVC geometries. Originality/value To the best of the authors’ knowledge, this review is the first of its kind to discuss extensively the computational progress in TVC development specific to gas turbine engines. Earlier review on TVC covers a wide variety of applications including land-based gas turbines, supersonic Ramjets, incinerators and hence compromise on the depth of analysis given to gas turbine engine applications. This review also comprehensively group the numerical studies based on geometry, flow and operating conditions.